Billionaire investor Kirk Kerkorian’s Tracinda Corp. on Wednesday boosted its stake in General Motors Corp. to 7.2 percent after it purchased 18.9 million shares as part of a tender offer launched last month.

Beverly Hills-based Tracinda’s purchase increases Kerkorian’s stake in GM to 40.9 million shares, or 7.2 percent, from 22 million shares, or 3.9 percent.

The purchase fell short of Tracinda’s original offer. In May, Kerkorian said he was offering about $870 million, or $31 per share. If all 28 million shares had been purchased, Kerkorian would have owned 8.8 percent of GM’s shares, or a total of 50 million. The offer expired on Tuesday evening.

GM’s board said last month that it was neutral when it came to Kerkorian’s plans to extend his stake in the automaker.